Question about numerals

I’m guessing Europeans and their ilk ustilize Arabic numerals because, well, most of the good math we enjoy today came to them from Arabs.

Why do the Arabs, then, use Indian numerals? What do Indians use?

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Well, Roman numerals don’t make any sense for arithmetic.

I don’t know anything about Indian numerals.

The system of numerals (“0, 1, 2, 3, 4, 5, 6, 7, 8, 9” + place notation) that we use today derives from the system developed by scribes in India in the first millenium. Can’t remember the exact date but somewhere between 600 and 800 A.D.

The scribes that invented this system are often credited with “inventing the number zero.” I suppose that’s one way to put it, but I think a better way to describe their incredible innovation is to say that they invented place notation. Under this system (now so familiar to us that we take it to granted) the value of a numeral depends not just on the character (whether a “5” or a “3”) but its location: i.e. whether it is in the “ones,” “tens,” or “ten thousands” position, etc.

Contrast this with the Roman Numeral System (and it’s predecessors in the west). In that system, each numerals value is independent of its place. “V” indicate 5 wherever it is.

One great thing about place notation is that it scales very well. With a very few symbols, you can represent vast numbers quite easily. Try writing 189,234,282 in roman numerals if you don’t believe me. Once they hit upon the idea of place notation, the concept of “zero” came about because they needed a symbol to show that a column (say in the number 101) was empty. At the very beginning, when writing, for example, 101, they would just make a dot in the tens column. Eventually this dot evolved into the 0 that we use today.

Another advantage, by the way, of these numerals, and place notation, is that you can do more complex operations such as mulitplication and division, my manipulating the symbols.

How did the Romans do mulitplication with Roman Numerals? They didn’t. They used a counting board (aka an abacus) to do these operations, and then wrote the result out in numerals.

This system of numerals passed to the west through Arabic mathematicians (who are themselves responsible for all kinds of brilliant innovations, such as algebra, logarithms and the concept of an algorithm). Hence it is called, improperly IMHO, “Arabic Numerals.” There is a movement afoot to call our system “Hindu-Arabic Numerals” in order to give credit to the Indians who created this numeral system.

Well into the Renaissance, several hundred years after Hindu-Arabic numerals were introduced into Europe, many persisted in using Roman numerals. Why Hindu-Arabic numerals took so long to catch on is a subject of some interest to those that study this sort of thing.

My own theory is that it comes down to the costs and benefits of learning and using each system. If you are a barely literate lower class person (i.e. if you are a typical European of the period) and most of what you do involves numbers less than say 50, then Hindu-Arabic numerals are not worth the trouble. In order to count to 10 using Hindu-Arabic numerals, you need to learn 10 different symbols, AND the somewhat tricky concept of place notation (we may not think it’s tricky because we learned it as children but it was actually a great innovation). Using Roman Numerals by contrast, you need only learn three symbols: “I,” “V,” and “X,” and you don’t have to worry about place notation.